I had been told that I did not qualify for this.

Here the important thing is to prove that the person in question is descended from a Sephardic Jew. This requires an analysis of the person's genealogy. The fact that a person qualifies or not, only means that the genealogist has a way to prove or not such ancestry. But once rejected by a genealogist, that does not mean that another genealogist with different tools cannot do it.